Several important problems in control theory can be reformulated as convex optimization problems. From duality theory in convex optimization, dual problems can be derived for these convex optimization problems. These dual problems can in turn be reinter-preted in control or system theoretic terms, often yielding new results or new proofs for existing results from control theory. Moreover, the m...

This paper focuses on implementation of a general canonical primal–dual algorithm for solving a class of fourth-order polynomial minimization problems. A critical issue in the canonical duality theory has been addressed, i.e., in the case that the canonical dual problem has no interior critical point in its feasible space Sa , a quadratic perturbation method is introduced to recover the global ...

In this paper two types of duals are considered for a class of variational problems involving higher order derivatives. The duality results are derived without any use of optimality conditions. One set of results is based on MondWeir type dual that has the same objective functional as the primal problem but different constraints. The second set of results is based on a dual of an auxiliary prim...

The design and implementation of a new algorithm for solving large nonlinear programming problems is described. It follows a barrier approach that employs sequential quadratic programming and trust regions to solve the subproblems occurring in the iteration. Both primal and primal-dual versions of the algorithm are developed, and their performance is illustrated in a set of numerical tests.

A dual for linear programming problems with fuzzy parameters is introduced and it is shown that a two person zero sum matrix game with fuzzy pay-o(s is equivalent to a primal-dual pair of such fuzzy linear programming problems. Further certain di6culties with similar studies reported in the literature are discussed.

Dual-primal FETI methods for linear elasticity problems in three dimensions are considered. These are nonoverlapping domain decomposition methods where some primal continuity constraints across subdomain boundaries are required to hold throughout the iterations, whereas most of the constraints are enforced by Lagrange multipliers. An algorithmic framework for dualprimal FETI methods is describe...

In this paper, a pair of Wolfe type nondifferentiable second order symmetric minimax mixed integer dual problems is formulated. Symmetric and self-duality theorems are established under η1bonvexity/η2-boncavity assumptions. Several known results are obtained as special cases. Examples of such primal and dual problems are also given.

We discuss assumptions on the constraint functions that allow constructive description of the geometry of a given set around a given point in terms of the constraints derivatives. Consequences for characterizing solutions of variational and optimization problems are discussed. In the optimization case, these include primal and primal-dual firstand second-order necessary optimality conditions.

We present primal-dual algorithms which give a 2.4 approximation for a class of node-weighted network design problems in planar graphs, introduced by Demaine, Hajiaghayi and Klein (ICALP’09). This class includes Node-Weighted Steiner Forest problem studied recently by Moldenhauer (ICALP’11) and other nodeweighted problems in planar graphs that can be expressed using (0, 1)-proper functions intr...

In this article, we construct a Fenchel-Lagrangian ε-dual problem for set-valued optimization problems by using the perturbation methods. Some relationships between the solutions of the primal and the dual problems are discussed. Moreover, an ε-saddle point theorem is proved.